Minimal quasi-stationary distribution approximation for a birth and death process

Abstract

In a first part, we prove a Lyapunov-type criterion for the $\xi \_1$-positive recurrence of absorbed birth and death processes and provide new results on the domain of attraction of the minimal quasi-stationary distribution. In a second part, we study the ergodicity and the convergence of a Fleming-Viot type particle system whose particles evolve independently as a birth and death process and jump on each others when they hit $0$. Our main result is that the sequence of empirical stationary distributions of the particle system converges to the minimal quasi-stationary distribution of the birth and death process.

The new version provides an original Lyapunov-type criterion for the $\xi \_1$-positive recurrence of a birth and death process. An original result on the domain of attraction of the minimal quasi-stationary distribution of a birth and death processes is also included. (26 pages)

References in corpus (1)

• Configurational transition in a Fleming-Viot-type model and probabilistic interpretation of Laplacian eigenfunctions